11,819 research outputs found
Signal Recovery in Perturbed Fourier Compressed Sensing
In many applications in compressed sensing, the measurement matrix is a
Fourier matrix, i.e., it measures the Fourier transform of the underlying
signal at some specified `base' frequencies , where is the
number of measurements. However due to system calibration errors, the system
may measure the Fourier transform at frequencies
that are different from the base frequencies and where
are unknown. Ignoring perturbations of this nature can lead to major errors in
signal recovery. In this paper, we present a simple but effective alternating
minimization algorithm to recover the perturbations in the frequencies \emph{in
situ} with the signal, which we assume is sparse or compressible in some known
basis. In many cases, the perturbations can be expressed
in terms of a small number of unique parameters . We demonstrate that
in such cases, the method leads to excellent quality results that are several
times better than baseline algorithms (which are based on existing off-grid
methods in the recent literature on direction of arrival (DOA) estimation,
modified to suit the computational problem in this paper). Our results are also
robust to noise in the measurement values. We also provide theoretical results
for (1) the convergence of our algorithm, and (2) the uniqueness of its
solution under some restrictions.Comment: New theortical results about uniqueness and convergence now included.
More challenging experiments now include
Closed orbit correction at synchrotrons for symmetric and near-symmetric lattices
This contribution compiles the benefits of lattice symmetry in the context of
closed orbit correction. A symmetric arrangement of BPMs and correctors results
in structured orbit response matrices of Circulant or block Circulant type.
These forms of matrices provide favorable properties in terms of computational
complexity, information compression and interpretation of mathematical vector
spaces of BPMs and correctors. For broken symmetries, a nearest-Circulant
approximation is introduced and the practical advantages of symmetry
exploitation are demonstrated with the help of simulations and experiments in
the context of FAIR synchrotrons
Development and implementation of an adaptive digital beamforming network for satellite communication systems
The use of adaptive digital beamforming techniques has, until recently, been largely restricted to high performance military radar systems. Recent advances in digital technology, however, have enabled the design of single chip digital beamforming networks. This, coupled with advances in digital signal processor technology, enables complete beamforming systems to be constructed at a lower cost, thus making the application of these techniques to commercial communications systems attractive. The design and development of such an adaptative digital beamforming network are described. The system is being developed as a proof of concept laboratory based demonstrator to enable the feasibility of adaptive digital beamforming techniques for communication systems to be determined. Ultimately, digital beamforming could be used in conjunction with large array antennas for communication satellite systems. This will enable the simultaneous steering of high gain antenna beams in the direction of gr...Peer ReviewedPostprint (published version
Four-dimensional light shaping: manipulating ultrafast spatio-temporal foci in space and time
Spectral dispersion of ultrashort pulses allows simultaneous focusing of
light in both space and time creating so-called spatio-temporal foci. Such
space-time coupling may be combined with existing holographic techniques to
give a further dimension of control when generating focal light fields. It is
shown that a phase-only hologram placed in the pupil plane of an objective and
illuminated by a spatially chirped ultrashort pulse can be used to generate
three dimensional arrays of spatio-temporally focused spots. Exploiting the
pulse front tilt generated at focus when applying simultaneous spatial and
temporal focusing (SSTF), it is possible to overlap neighbouring foci in time
to create a smooth intensity distribution. The resulting light field displays a
high level of axial confinement, with experimental demonstrations given through
two-photon microscopy and non-linear laser fabrication of glass
Focal-plane wavefront sensing with high-order adaptive optics systems
We investigate methods to calibrate the non-common path aberrations at an
adaptive optics system having a wavefront-correcting device working at an
extremely high resolution (larger than 150x150). We use focal-plane images
collected successively, the corresponding phase-diversity information and
numerically efficient algorithms to calculate the required wavefront updates.
The wavefront correction is applied iteratively until the algorithms converge.
Different approaches are studied. In addition of the standard Gerchberg-Saxton
algorithm, we test the extension of the Fast & Furious algorithm that uses
three images and creates an estimate of the pupil amplitudes. We also test
recently proposed phase-retrieval methods based on convex optimisation. The
results indicate that in the framework we consider, the calibration task is
easiest with algorithms similar to the Fast & Furious.Comment: 11 pages, 7 figures, published in SPIE proceeding
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